Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;

import static java.lang.System.out;

/**
 * @author artyom
 */
public class FunkyNumbersFast {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		long a = sc.nextLong();
		long m = ((long) Math.sqrt(8 * a + 1) - 1) / 2;
		long c = 8 * a + 1;
		for (long i = 1; i <= m; i++) {
			long sq = c - 4 * i * (i + 1);
			long r = (long) Math.sqrt(sq);
			if (r * r == sq && r > 1) {
				out.println("YES");
				return;
			}
		}

		out.println("NO");
	}
}